As some may know, I worked with Gaffney on the 911 Mystery Plane book putting together the RADES and FAA radar data (among other things). If I recall correctly, WORD31 took off before the arrival of AAL77 and headed pretty much straight towards Offutt AFB with a standard Camp Springs One departure (followed by GOFER06). Nothing sinister about that since Offutt is where the plane was based. Also, another E4B was 'stuck' on the ground which we have ATC audio for (I don't recall the AFB off hand).
So after the Pentagon was hit, it made sense that they would want to get the 'stand by' E4B in the air as rapidly as possible. Once airborne and flying in unrestricted airspace (it never did enter restricted airspace), it was diverted south to support AF1 which was originally headed back to DC from Florida. However, that plan changed when AF1 changed course to the west, at which time VENUS77 took up a holding pattern south of DC over NC. When AF1 headed on to Offutt, VENUS77 followed.
At no point was an E4B 'flying around the Pentagon'. With 4 local ASR's and 3 ARSR radars covering the DC area, it would be close to impossible to cover up a 747 (even with anti-reflective paint) signature. Not to mention the plane would have to talk to the ATC at Andrews and/or DCA at some point.
I know it is fun to speculate, but the truth is rather mundane. Command and control was under attack, so airborne command and control was put up ASAP. I would be more alarmed if they had not put up the E4B.